Hybrid laplace transform solution for coupled partial differential equation of fumigant transport in stored grain

Abstract

The research presented in this dissertation is a mathematical solution of hybrid analytical and numerical simulation approach to the model of coupled partial linear differential equations of grain stored fumigation. The model is partly adopted based on phenomena of advection-diffusion transport process of solute mass for the fumigation distribution of phosphine gas concentration in a cylindrical silo containing grain. One dimensional advection diffusion coupled of partial linear differential equation is solved using Laplace transform by applied numerical simulation of Week’s method of Laplace inverse (WLI) and finite difference method (FDM) while Octave software is used in the simulation. The developed WLI algorithm results verified using Cauchy test for convergence on FDM error results. However, the FDM error shows that to have better results of FDM, need a smaller step size increment ???. The error results also showed that the higher fumigant concentration (????=10 mg/L) injected to the silo, the higher relative error in the solution of concentration of phosphine gas and concentration in the grain obtained, when compared with ????=5 mg/L. Furthermore, the investigation on efficiency of phosphine gas concentration during fumigation based on graph of the results showed that, the length of the time phosphine gas concentration could be taken for covering the silo is independent of the amount of boundary fumigant concentration (BFC) injected to the silo. While for concentration in the grain inside the silo, the time is depending on the BFC, where the higher fumigant concentration in the silo, the higher concentration received by the grain. Besides that, when the velocity of the model increase, the time taking for phosphine gas concentration during fumigation is reduced. In addition, the higher the velocity of the model and less amount of BFC, then the least amount of concentration the grain absorbs during the fumigation processes.